/*
 * Copyright (c) 2015 Typelevel
 *
 * Permission is hereby granted, free of charge, to any person obtaining a copy of
 * this software and associated documentation files (the "Software"), to deal in
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 * use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
 * the Software, and to permit persons to whom the Software is furnished to do so,
 * subject to the following conditions:
 *
 * The above copyright notice and this permission notice shall be included in all
 * copies or substantial portions of the Software.
 *
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS
 * FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
 * COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER
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 */

package algebra
package ring

/**
 * A Boolean ring is a ring whose multiplication is idempotent, that is
 * `a⋅a = a` for all elements ''a''. This property also implies `a+a = 0`
 * for all ''a'', and `a⋅b = b⋅a` (commutativity of multiplication).
 *
 * Every Boolean ring is equivalent to a Boolean algebra.
 * See `algebra.lattice.BoolFromBoolRing` for details.
 */
trait BoolRing[A] extends Any with BoolRng[A] with CommutativeRing[A]

object BoolRing extends RingFunctions[BoolRing] {
  @inline final def apply[A](implicit r: BoolRing[A]): BoolRing[A] = r
}
